heapq 模块提供了堆算法。heapq是一种子节点和父节点排序的树形数据结构。这个模块提供heap[k] <= heap[2*k+1] and heap[k] <= heap[2*k+2]。为了比较不存在的元素被人为是无限大的。heap最小的元素总是[0]。
打印 heapq 类型
import math import random from cStringIO import StringIO def show_tree(tree,total_width=36,fill=' '): output = StringIO() last_row = -1 for i,n in enumerate(tree): if i: row = int(math.floor(math.log(i+1,2))) else: row = 0 if row != last_row: output.write('\n') columns = 2**row col_width = int(math.floor((total_width * 1.0) / columns)) output.write(str(n).center(col_width,fill)) last_row = row print output.getvalue() print '-' * total_width print return data = random.sample(range(1,8),7) print 'data: ',data show_tree(data)
打印结果
data: [3,2,6,5,4,7,1] 3 2 6 5 4 7 1 ------------------------- heapq.heappush(heap,item)
heap = [] data = random.sample(range(1,data for i in data: print 'add %3d:' % i heapq.heappush(heap,i) show_tree(heap)
打印结果
data: [6,1,3,2] add 6: 6 ------------------------------------ add 1: 1 6 ------------------------------------ add 5: 1 6 5 ------------------------------------ add 4: 1 4 5 6 ------------------------------------ add 3: 1 3 5 6 4 ------------------------------------ add 7: 1 3 5 6 4 7 ------------------------------------ add 2: 1 3 2 6 4 7 5 ------------------------------------
根据结果可以了解,子节点的元素大于父节点元素。而兄弟节点则不会排序。
heapq.heapify(list)
将list类型转化为heap,在线性时间内,重新排列列表。
print 'data: ',data heapq.heapify(data) print 'data: ',data show_tree(data)
打印结果
data: [2,1] data: [1,4] 1 3 2 7 6 5 4 ------------------------------------ heapq.heappop(heap)
删除并返回堆中最小的元素,通过heapify() 和heappop()来排序。
data = random.sample(range(1,data heapq.heapify(data) show_tree(data) heap = [] while data: i = heapq.heappop(data) print 'pop %3d:' % i show_tree(data) heap.append(i) print 'heap: ',heap
打印结果
data: [4,2] 1 4 2 7 5 6 3 ------------------------------------ pop 1: 2 4 3 7 5 6 ------------------------------------ pop 2: 3 4 6 7 5 ------------------------------------ pop 3: 4 5 6 7 ------------------------------------ pop 4: 5 7 6 ------------------------------------ pop 5: 6 7 ------------------------------------ pop 6: 7 ------------------------------------ pop 7: ------------------------------------ heap: [1,7]
可以看到已排好序的heap。
heapq.heapreplace(iterable,n)
data = random.sample(range(1,data heapq.heapify(data) show_tree(data) for n in [8,9,10]: smallest = heapq.heapreplace(data,n) print 'replace %2d with %2d:' % (smallest,n) show_tree(data)
打印结果
data: [7,1] 1 2 3 5 6 7 4 ------------------------------------ replace 1 with 8: 2 5 3 8 6 7 4 ------------------------------------ replace 2 with 9: 3 5 4 8 6 7 9 ------------------------------------ replace 3 with 10: 4 5 7 8 6 10 9 ------------------------------------
heapq.nlargest(n,iterable) 和 heapq.nsmallest(n,iterable)
返回列表中的n个最大值和最小值
data = range(1,6) l = heapq.nlargest(3,data) print l # [5,3] s = heapq.nsmallest(3,data) print s # [1,3]
PS:一个计算题
构建元素个数为 K=5 的最小堆代码实例:
#!/usr/bin/env python # -*- encoding: utf-8 -*- # Author: kentzhan # import heapq import random heap = [] heapq.heapify(heap) for i in range(15): item = random.randint(10,100) print "comeing ",item,if len(heap) >= 5: top_item = heap[0] # smallest in heap if top_item < item: # min heap top_item = heapq.heappop(heap) print "pop",top_item,heapq.heappush(heap,item) print "push",else: heapq.heappush(heap,item) print "push",pass print heap pass print heap print "sort" heap.sort() print heap
结果: